Logarithm Algebra (Power Property) - To Answer (Coefficient N)

Level 1

This math topic focuses on applying the power property of logarithms to algebraic expressions to solve for specific variables such as 'r', 't', 'y', 'n', and 'm'. Questions involve simplifying logarithmic expressions and equating them to given logarithms, thus requiring learners to isolate and solve the variable. The problems are set with multiple-choice answers, emphasizing the practical application and computational aspects of logarithm functions within an advanced mathematics context. This is designed to enhance understanding and proficiency in logarithm properties and algebraic manipulation.

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Logarithm Algebra (Power Property) - To Answer (Coefficient N) Worksheet

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Logarithm Algebra (Power Property) - To Answer (Coefficient N)
1
Use the power rule to simplify this and solve for 'r'
A LaTex expression showing 4\log sub 5 (-1r + 2) = \log sub 5 (4)
a A LaTex expression showing r=2
b A LaTex expression showing r=3
c A LaTex expression showing r=0
2
Use the power rule to simplify this and solve for 'r'
A LaTex expression showing 2\log sub 2 (r + 7) = \log sub 2 (1)
a A LaTex expression showing r=-4
b A LaTex expression showing r=-6
c A LaTex expression showing r=-10
3
Use the power rule to simplify this and solve for 't'
A LaTex expression showing 2\log sub 8 (-1t - 8) = \log sub 8 (9)
a A LaTex expression showing t=-14
b A LaTex expression showing t=-11
c A LaTex expression showing t=-6
4
Use the power rule to simplify this and solve for 'y'
A LaTex expression showing 4\log sub 8 (y - 5) = \log sub 8 (1)
a A LaTex expression showing y=3
b A LaTex expression showing y=15
c A LaTex expression showing y=6
5
Use the power rule to simplify this and solve for 'n'
A LaTex expression showing 2\log sub 9 (-1n + 1) = \log sub 9 (4)
a A LaTex expression showing n=-2
b A LaTex expression showing n=2
c A LaTex expression showing n=-1
6
Use the power rule to simplify this and solve for 'm'
A LaTex expression showing 2\log sub 7 (-4m - 2) = \log sub 7 (4)
a A LaTex expression showing m=-2
b A LaTex expression showing m=-1
c A LaTex expression showing m=5
7
Use the power rule to simplify this and solve for 't'
A LaTex expression showing 3\log sub 2 (t - 3) = \log sub 2 (4)
a A LaTex expression showing t=-5
b A LaTex expression showing t=5
c A LaTex expression showing t=14
8
Use the power rule to simplify this and solve for 't'
A LaTex expression showing 2\log sub 9 (-1t - 3) = \log sub 9 (1)
a A LaTex expression showing t=-12
b A LaTex expression showing t=2
c A LaTex expression showing t=-4